They're not claiming to get energy from nothing. They're just saying that the energy they got out from the fusion reactions exceeded the energy require to initiate the fusion.

Consider a matchstick. When it is burning, you get energy out of it, but in order to start it burning in the first place, you have to put energy into the system (by dragging it across a friction strip, heating the match head to its autoignition temperature). You end up getting more energy out (flame) than you put into it by striking the match, but this energy doesn't come from nowhere--it comes from converting the chemical energy of the matchstick to heat-energy.

The fusion scientists basically figured out a more efficient way to strike the match, so that the energy they liberated from the fuel exceeded the energy required to get the fusion reaction happening in the first place.

Fusion is not a source of infinite energy, because there is not an infinite amount of fuel available. You can't burn a matchstick twice.

Some of the mass-energy of the fusing nuclei is converted into heat-energy. The total amount of energy is still the same. You're not getting energy for free, you're converting one kind of energy into another.